$(50pts),$ Water at $25C$ drains from a large tank, by gravity, through a pipe. The outlet of the drain pipe is open to the atmosphere, and is located $7\mathrm{.}23$ m below the surface of the large tank. The pipe itself is $5\mathrm{.}66$ m long and $2\mathrm{.}35$ cm in diameter. The average surface roughness height inside the pipe is $0\mathrm{.}0540$ mm $.$ The pipe inlet at the tank is a reentrant inlet. There are two smooth $90$ threaded elbows in the pipe. Note: Use the Churchill equation, not the Colebrook equation.

$($a$)$ Estimate the volume flow rate in $\frac{L}{m}in.$ Note: You may need to iterate. I strongly suggest using software to solve this problem. However, show a sketch with your chosen control volume and show the equations you use, etc., even if you solve this problem with software.

$($b$)$ Repeat, except ignore minor losses in the piping system. Calculate the percentage error caused by this approximation.